date and time created 85/09/06 17:52:36 by zliu

SCCS-vsn: lib/libm/common_source/acosh.c 1.1

diff --git a/usr/src/lib/libm/common_source/acosh.c b/usr/src/lib/libm/common_source/acosh.c
new file mode 100644 (file)
index 0000000..e4b008e
--- /dev/null
+++ b/usr/src/lib/libm/common_source/acosh.c
@@ -0,0 +1,83 @@
+/* 
+ * Copyright (c) 1985 Regents of the University of California.
+ * 
+ * Use and reproduction of this software are granted  in  accordance  with
+ * the terms and conditions specified in  the  Berkeley  Software  License
+ * Agreement (in particular, this entails acknowledgement of the programs'
+ * source, and inclusion of this notice) with the additional understanding
+ * that  all  recipients  should regard themselves as participants  in  an
+ * ongoing  research  project and hence should  feel  obligated  to report
+ * their  experiences (good or bad) with these elementary function  codes,
+ * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)acosh.c    1.1 (ELEFUNT) %G%";
+#endif not lint
+
+/* ACOSH(X)
+ * RETURN THE INVERSE HYPERBOLIC COSINE OF X
+ * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
+ * CODED IN C BY K.C. NG, 2/16/85;
+ * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
+ *
+ * Required system supported functions :
+ *     sqrt(x)
+ *
+ * Required kernel function:
+ *     log1p(x)                ...return log(1+x)
+ *
+ * Method :
+ *     Based on 
+ *             acosh(x) = log [ x + sqrt(x*x-1) ]
+ *     we have
+ *             acosh(x) := log1p(x)+ln2,       if (x > 1.0E20); else           
+ *             acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
+ *     These formulae avoid the over/underflow complication.
+ *
+ * Special cases:
+ *     acosh(x) is NaN with signal if x<1.
+ *     acosh(NaN) is NaN without signal.
+ *
+ * Accuracy:
+ *     acosh(x) returns the exact inverse hyperbolic cosine of x nearly 
+ *     rounded. In a test run with 512,000 random arguments on a VAX, the
+ *     maximum observed error was 3.30 ulps (units of the last place) at
+ *     x=1.0070493753568216 .
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ */
+
+#ifdef VAX     /* VAX D format */
+/* static double */
+/* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
+/* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
+static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
+static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
+#define    ln2hi    (*(double*)ln2hix)
+#define    ln2lo    (*(double*)ln2lox)
+#else  /* IEEE double */
+static double
+ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
+ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
+#endif
+
+double acosh(x)
+double x;
+{      
+       double log1p(),sqrt(),t,big=1.E20; /* big+1==big */
+
+#ifndef VAX
+       if(x!=x) return(x);     /* x is NaN */
+#endif
+
+    /* return log1p(x) + log(2) if x is large */
+       if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} 
+
+       t=sqrt(x-1.0);
+       return(log1p(t*(t+sqrt(x+1.0))));
+}